The closest we can actually get to most real numbers is to compute a
rational number that is as close as we need. It can be shown that
rational numbers are dense in the real numbers; that is,
between every two real numbers there is a rational number, and between
every two rational numbers is a real number.3.1An irrational number can be defined as any real
number having a non-repeating decimal expansion. For example,
is an irrational real number whose decimal expansion starts
out as3.2

Every truncated, rounded, or repeating expansion is a
rational number. That is, it can be rewritten as an integer
divided by another integer. For example,

and, using
to denote the repeating part of a
decimal expansion, a repeating example is as follows: